Harry and Xylia has some money each. If Xylia gives Harry $16, he will have 3 times as much money as her. If Harry gives Xylia $19, he will have the same amount of money as her. How much money does each person have respectively?
- Harry?
- Xylia?
|
Case 1 |
Case 2 |
|
Harry |
Xylia |
Harry |
Xylia |
Before |
3 u - 16 |
1 u + 16 |
2 u + 19 |
2 u - 19 |
Change |
+ 16 |
- 16 |
- 19 |
+ 19 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Xylia gives Harry some money or Harry gives Xylia some money, the total amount of money remains the same.
Total amount that Harry and Xylia have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Harry and Xylia each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Harry has at first in Case 1 and Case 2 is the same.
3 u - 16 = 2 u + 19
3 u - 2 u = 19 + 16
1 u = 35
Amount that Harry has
= 2 u + 19
= 2 x 35 + 19
= 70 + 19
= $89
(b)
Amount that Xylia has
= 1 u + 16
= 35 + 16
= $51
Answer(s): (a) $89; (b) $51